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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Area

Betty needs to buy carpeting to cover her entire bedroom floor, which is 12 ft. long and 8 ft. wide. How much carpeting does she need to buy?

Possible Answers:

$40\ \textup{sq.\ ft.}$

$120\ \textup{sq.\ ft.}$

$96\ \textup{sq.\ ft.}$

$20\ \textup{sq.\ ft.}$

$4\ \textup{sq.\ ft.}$

Correct answer:

$96\ \textup{sq.\ ft.}$

Explanation:

Remember to use the formula below to find area:

$Area=length\cdot width$

Since Betty needs carpeting to cover her floor, this problem asks you to find the area. This means you need to multiply length and width to find the area, which is given in square feet, since each foot of carpeting is not only one foot long, but also one foot wide (a square).

Step 1: plug in the numbers for length and width

$Area=12\cdot8$

Step 2: solve

Area=96 sq. ft.

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Example Question #2 : Area

Untitled

The rectangle in the above figure has length 20 and height 10. What is the area of the red region?

Possible Answers:

$200 - 5 \pi$

175

150

$200 - \frac{5}{2} \pi$

Insufficient information is given to determine the area.

Correct answer:

175

Explanation:

The red region is formed by removing a triangle from a rectangle.

The rectangle measures 20 by 10, and, subsequently, has area

$20 \cdot 10 = 200$ .

The triangle has base 10. Its height is the radius of the circle, which is 5, so its area is

$\frac{1}{2} \cdot 10 \cdot 5 = 25$ .

The difference between the areas, which is the area of the red region, is 200 - 25 = 175 .

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Example Question #3 : Area

Untitled_2

The rectangle in the above figure has length 20 and height 10. What is the area of the red region?

Possible Answers:

Insufficient information is given to determine the area.

250

$200 + 5 \pi$

$200 + \frac{5}{2} \pi$

225

Correct answer:

225

Explanation:

The red region is a composite of two figures:

One is a rectangle measuring 20 by 10, which, subsequently, has area

$20 \cdot 10 = 200$ .

The other is a triangle with base 10. Its height is the radius of the circle, which is 5, so its area is

$\frac{1}{2} \cdot 10 \cdot 5 = 25$ .

The sum of the areas, which is the area of the red region, is 200 + 25 = 225 .

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Example Question #2 : Area Of A Rectangle Or Square

Thompson High School wants to buy artificial turf for their practice soccer field. The field is 150 ft by 100 ft. How much turf should they buy?

Possible Answers:

$\small 10\textup{,}000\ \textup{ft}^{2}$

$\small 15\textup{,}000\ \textup{ft}^{2}$

$\small 1500\ \textup{ft}^{2}$

$\small 1000\ \textup{ft}^{2}$

$\small 150\textup{,}000\ \textup{ft}^{2}$

Correct answer:

$\small 15\textup{,}000\ \textup{ft}^{2}$

Explanation:

Recall, the area of a rectangle = length x width

Next, plug in the two values given in the problem

$\small Area = 150 *100 = 15000$

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Example Question #5 : Area Of A Rectangle Or Square

Judy needs to buy a glass table cover for a dinner party, which is 8 ft. long and 3 ft. wide. How much glass does she need to buy?

Possible Answers:

$5\ \textup{ft}^{2}$

$32\ \textup{ft}^{2}$

$11\ \textup{ft}^{2}$

$36\ \textup{ft}^{2}$

$24\ \textup{ft}^{2}$

Correct answer:

$24\ \textup{ft}^{2}$

Explanation:

Explanation:

Remember to use the formula below to find area:

$Area = length\cdot width$

Since Judy needs enough glass to cover the whole table, this problem asks you to find the area. This means you need to multiply length and width to find the area, which is given in square feet, since each foot of glass is not only one foot long, but also one foot wide (a square).

Step 1: Plug in the numbers for the length and width

$Area = 8 \cdot 3$

Step 2: Solve

Area = 24 sq. ft.

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Example Question #3 : Area Of A Rectangle Or Square

Jessica's blanket is 12 square feet. Lisa has a blanket that is half the size of Jessica's blanket. Which of the following are possible dimensions of Lisa's blanket?

Possible Answers:

$3\ ft\times3\ ft$

$1\ ft\times12\ ft$

$3\ ft\times2\ ft$

$2\ ft\times2\ ft$

Correct answer:

$3\ ft\times2\ ft$

Explanation:

The area of a rectangle if found by multiplying the length times the width. Here, we know that Lisa's blanket is half the area of Jessica's blanket. Since Jessica's blanket is 12 square feet, that means that Lisa's blanket must be 6 square feet.

The only length and width values that give us 6 square feet when multiplied by one another are 3 feet by 2 feet. This is therefore the correct answer.

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Example Question #4 : Area Of A Rectangle Or Square

Jon built a new garden with two sides equalling $15\textup{ ft}$ , and the other sides equalling $10\textup{ ft}$ . What is the area of Jon's new garden?

Possible Answers:

$150\textup{ ft}^{2}$

$100\textup{ ft}$

$100\textup{ ft}^{2}$

$225\textup{ ft}^{2}$

$150\textup{ ft}$

Correct answer:

$150\textup{ ft}^{2}$

Explanation:

In order to do this problem you must imagine the garden as a rectangle with sides of 10ft by 15ft by 10ft by 15ft .

The formula for area of a rectangle is $A=l\cdot w$ .

In our case the length is 10 and the width is 15. To find the area of a rectangle you must multiply 10ft by 15ft , which equals 150ft^2

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Example Question #1 : Geometry

The area of the following rectangle is $48\: cm^2$ . Solve for .

Possible Answers:

x=12

x=4

x=16

x=8

Correct answer:

x=4

Explanation:

The area of a rectangle can be found by multiplying the length by the width.

$A=l\times w$

$48=3x\times x=3x^2$

48=3x^2

$\frac{48}{3}=\frac{3x^2}{3}$

16=x^2

$\sqrt{16}=\sqrt{x^2}$

4=x

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Example Question #4 : Area Of A Rectangle Or Square

A square has a perimeter of 16in . What is its area?

Possible Answers:

8in^2

16in^2

64in^2

4in^2

Correct answer:

16in^2

Explanation:

A square with a perimeter of 16in has equal sides whose lengths add up to . You could figure out what these sides have to be in a lot of different ways. If you use algebra, you might set up an equation like x+x+x+x=16 or 4x=16 . You would figure out that the side lengths must all be . If a square has side lengths of inches, to figure out the area you would do 4*4 , or 4^2 , and you would get an answer of .

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Example Question #5 : Area Of A Rectangle Or Square

A square has a perimeter of 76 cm . What is its area?

Possible Answers:

$76cm^{2}$

Not enough information given to solve.

$361 cm^{2}$

$38cm^{2}$

$152cm^{2}$

Correct answer:

$361 cm^{2}$

Explanation:

A square has a perimeter of 76 cm . The four sides of any square are equal in length, so to find one side of the square, we divide the perimeter by .

$76cm \div4=19 cm$

The area of a square is length x width, and in this case side x side:

$19cm \times 19cm = 361cm^{2}$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #1 : Area

Example Question #2 : Area

Example Question #3 : Area

Example Question #2 : Area Of A Rectangle Or Square

Example Question #5 : Area Of A Rectangle Or Square

Example Question #3 : Area Of A Rectangle Or Square

Example Question #4 : Area Of A Rectangle Or Square

Example Question #1 : Geometry

Example Question #4 : Area Of A Rectangle Or Square

Example Question #5 : Area Of A Rectangle Or Square

All Pre-Algebra Resources

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